Question: Simplify the following expression: $ x = \dfrac{-10z + 4}{z - 4} + \dfrac{-3}{2} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-10z + 4}{z - 4} \times \dfrac{2}{2} = \dfrac{-20z + 8}{2z - 8} $ Multiply the second expression by $\dfrac{z - 4}{z - 4}$ $ \dfrac{-3}{2} \times \dfrac{z - 4}{z - 4} = \dfrac{-3z + 12}{2z - 8} $ Therefore $ x = \dfrac{-20z + 8}{2z - 8} + \dfrac{-3z + 12}{2z - 8} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-20z + 8 - 3z + 12}{2z - 8} $ $x = \dfrac{-23z + 20}{2z - 8}$